Polygon Limit Exploration (Archimedes Method)
- Author:
- Auston B Cron
Looking at LTF Polygons in a Circle, this applet will assist in completing the exercise.
The circle on the screen is a unit circle; however, you can change the radius to match any value you measure up to 8 units. The table will give the results up to a 100-gon.
Table format from LTF activity on Limits of a Polygon in a Circle (NMSI Module 16 of LTF).
Triangle ABC is triangle formed by the point A and any side of the polygon. The area of the polygon is the number of sides times the area of Triangle ABC.
If you expand the radius of the circle and can no longer see the figure, click mouse on point A and scroll the figure in and out...
As the perimeter of the polygon approaches a circle, the ratio of the perimeter to diameter approached what well known value? ____________
Excellent Resource: http://www.mathopenref.com/polygonregular.html
Member access to LTF modules: http://www.ltftraining.org/instructionalresources/Math/LessonsOverviews/tabid/271/Default.aspx?grade=High+School
Archimedes Method for Pi